(a)
To graph: the given function
(a)
Explanation of Solution
Given:
The function is
Concept used:
The slope of the tangent to a curve
The tangent to be horizontal so the slope should be equal to 0
That is
Calculation:
The function is
Draw the table
Test one point in each of the region formed by the graph
If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function
Draw the graph
(b)
To explain:
The shape of the graph by computing the limit as the given function.
(b)
Answer to Problem 58E
Explanation of Solution
Given:
The function
Concept used:
The definition of a vertical cusp is that the one sided limits of the derivative approach opposite
: positive infinity on one side and negative infinity on the other side . A vertical tangent has the one sided limits of the derivative equal to the same sign of infinity
The derivative at the relevant point is undefined in both the cusp and the vertical tangent
Calculation:
The function is
Taking limit on both sides
(c)
To find:
The maximum and minimum values and the exact values.
(c)
Answer to Problem 58E
The maximum value is
Explanation of Solution
Given:
The function
Concept used:
The slope of the tangent to a curve
The tangent to be horizontal so the slope should be equal to 0
That is
Calculation:
The function is
Differentiating equation (1) with respect to
For maximum value and minimum value is
The minimum value is at
(d)
To find:
The
(d)
Answer to Problem 58E
Explanation of Solution
Given:
The function
Concept used:
The definition of a vertical cusp is that the one sided limits of the derivative approach opposite
: positive infinity on one side and negative infinity on the other side . A vertical tangent has the one sided limits of the derivative equal to the same sign of infinity
The derivative at the relevant point is undefined in both the cusp and the vertical tangent
Calculation:
The function is
Differentiating equation (1) with respect to
Again differentiating equation (2) with respect to
The vertical tangent means that the derivative at that point approaches infinity
Since the slope is infinitely large .
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning